id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6139	Samraiz, Muhammad; Qasim, Muhammad ; Rahman, Gauhar ; Sarwar, Muhammad ; Fatima, Nahid ; Abodayeh, Kamaleldin 	Trapezoidal and Midpoint-type Inequalities Based on Extended Conformable Operators	2025	34	.pdf	application/pdf	11923	667	77	Math, 18 (4) (2025), 6139 6 of 34 Again, we apply the technique of integration by parts to the second term; therefore, we obtain the following expression I1 = η ω − ν h′ ( η − 1 η ν + 1 η ω )∫ 1 0 ( 1 (kµ) α k − ( 1− (1− φ)µ kµ )α k ) dφ + ( η ω − ν )2 h(ν) 1 (ku) α k − ( η ω − ν )2 1 k (α k )∫ 1 0 [ 1− (1− t)µ kµ ]α k −1 (1− t)µ−1 × h ( η − t η ν + t η ω ) α k ) dφ + ( η ω − ν )2 h(ν) 1 (ku) α k − ( η ω − ν )µα k +2 ( Γ ( α k + 1 ) k.k α k −1Γ(αk ) ) × ∫ (η−1)ν+ω η ν  ( ω−ν η )µ − ( (η−1)ν+ω η − x )µ µ  α k −1	cache/ejpam-6139.pdf	txt/ejpam-6139.txt